Abstract
In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.
Original language | English |
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Pages (from-to) | 879-898 |
Number of pages | 20 |
Journal | Journal of Optimization Theory and Applications |
Volume | 186 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2020 |
Bibliographical note
Publisher Copyright:© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Hadamard manifolds
- Multiobjective optimization
- Pareto optimality
- Proximal point methods
- Quasiconvex function